Which of the following numbers is a multiple of 8? ${42,58,69,88,99}$
Solution: The multiples of $8$ are $8$ $16$ $24$ $32$ ..... In general, any number that leaves no remainder when divided by $8$ is considered a multiple of $8$ We can start by dividing each of our answer choices by $8$ $42 \div 8 = 5\text{ R }2$ $58 \div 8 = 7\text{ R }2$ $69 \div 8 = 8\text{ R }5$ $88 \div 8 = 11$ $99 \div 8 = 12\text{ R }3$ The only answer choice that leaves no remainder after the division is $88$ $ 11$ $8$ $88$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $88$ $88 = 2\times2\times2\times11 8 = 2\times2\times2$ Therefore the only multiple of $8$ out of our choices is $88$. We can say that $88$ is divisible by $8$.